E2. Dean bungee (1) As part of a fundraiser, you want the new dean

E2. Dean bungee (1) As part of a fundraiser, you want the new dean to bungee jump from a crane. The jump will be made from 44 m above a 2.5 m deep pool of Jello. A 30 m long bungee cord would be attached to the dean's ankle. You must convince the dean that your plan is safe for a person of his mass, 70 kg. As the bungee cord stretches, it will exert a force with the same properties as the force exerted by a spring. Your plan has the dean stepping off a platform and being in free fall for the 30 m before the cord begins to stretch. You must determine the elastic constant of the bungee cord so that it stretches only 12 m, which will keep the dean's head just out of the Jello. E4. Navy plane (3) The Navy wants a new airplane launcher for their aircraft carriers that is basically a large spring and your job is to determine the necessary spring constant. The launcher pushes the plane for a short distance along a much longer runway. During that same time, the plane's jet engines supply a constant thrust force for the entire length of the runway. The planes need to have a minimum velocity by the time they reach the end of the runway in order to take off successfully. In order to do the above problems, you need to know the following beside what you have learned in class so far. Potential energy of spring – the stiffness of a spring is characterized by its spring constant, k, (larger the k, the stiffer it is). If its potential energy is chosen to be zero when it is in its natural length (not stretched, not compressed), when it is either stretched OR compressed the potential energy is given by !
𝑈! (𝑥) = 𝑘(𝑥 − 𝑥! )! , where 𝑥 is the length of the spring and 𝑥! is its natural length. !
The thrust of the engine used to describe the Navy plane problem works just like gravity (and therefore it’s a kind of force), but in the horizontal direction. It would accelerate the plane at a constant rate if no other forces (influences) are at work. As a result, it will produce the same effect as gravitational fall, and 𝐸!" = 𝐹!"#$%! ∆𝑥, where ∆𝑥 is the distance that the plane is pushed by the thrust. If you do this problem in COACH, you have to say you use forces, and choose spring force and thrust (both in the direction of the motion). Also you need to choose “airplane and spring” for the system (objects to consider for energy conservation) so that potential energy is used for the spring, rather than Ein or Eout for this. It will let you proceed if you choose just the plane, but then you will have to deal with forces fully, and that’s not what you want to do.